MRT supply networks can be divided into the traction substation, the go-circuit and the return-circuit. In this thesis, a three-stage optimisation schema is formulated to represent both the normal condition and failure conditions. The technique of Pareto-optimal set is developed for go-circuit and return-circuit optimisation.The optimisation of energy consumption and load sharing in the go-circuit cannot be obtained simultaneously. The effects of headway, synchronisation delay and dwell time on go-circuit are investigated.The improvement of touch voltage or stray current in return-circuit tends to deteriorate the other. Different earthing and bonding arrangements are extensively explored. Three evolutionary algorithms are applied for the multi-objective optimisation in MRT system: the Multi-Objective Genetic Algorithm (MOGA) for discrete problems, Multi-Objective Particle Swarm (MOPS) algorithm and Multi-Objective Differential Evolution (MODE) algorithm for continuous problems. MOPS and MODE are proposed to solve MRT problems for the first time.